Spiral bevel gear



Feb. 2 5, 1930. E. WILDHABER 1,743,813

' SPIRAL BBVEL GEAR Filed Jan. 25, 1924 s Sheets-Sheet 1 g F W v 4" 9 vv A ERNEfiT WILDH ABEFL 'roR BY MIL,

-30. ATTORNEY- E. WILDHABER 1,748,813

a SPIRAL BEVEL GEAR Filed Jan. 25, 1924 5 Sheets-Sheet 5 KWQ/4ZIINVENTOR E Wildlwber g BY j ATTORNEY enema Fa. 2 1936".

TE T ERNEST WILDI-IABEB, on NEW YOR ROCHESTER, NEW YORK, A

on. Y.,i assrenon' *ro eLEAsoN, wo

a I a v 32's, or" conronarron orlnnw YORK v SPIRAL BE EL GEAR:Appiieationfihd January 25, 1924. Seria1 mjeasm. 5 I

My invention refers to bevel' gears with longitudinally curved teeth,and particularly to bevel gears whose tooth surfaces are either surfacesof revolution, .or more fre- 5 quently such composite surf-aces, as maybe derived from a surface of revolution by'a rolling-generating vaction. The methods referredto consist in providing arotary cutting tooltooth space of ablank.

Hitherto standard spir been made by; cutting tooth side after toothside, one side only being out at a time. Another known method permitscutting both sides of a tooth space on one gear of a pairsimultaneously, while the other gear requires separate cuts-for eachside. Thi

productionis bought with a certain sacrifice on the tooth shape, theteeth ofone gearbeing tapered only to a small extent, in longitudinaldirection, while the required taper is carried mainly by the teeth ofsaid pair. In other words the teeth and the tooth spaces are differentlytapered in such gears. The angular width'of space-varies with thedistance from the apex,

One object of my invention is to provide aspiral-bevel gear withsubstantially constant angular width ofspace, having such a tooth shape,that both sides ofa' tooth space can be simultaneously formed with arotary cutting tool, sa-i d cutt gitudinally circular cutting face. v

A further object is to provide a spiral bevel gear with teethequallycurved in longitudinal direction, the degree of curvature being such,that Ybot h sides of atooth space of uniform angular w a1 bevel gearshave dth can be simultanetool.

Another pu vide a spiral bevel gearhaving a substantially constantangular width inclined tooth bottom of sub stant actualwidth.

. A still further pur to provide.a'pairof spiral bevel. gears, in whichboth sides of a tooth space may be simultaneously cut or ground oneither gear ofsa'idpair.- Y

stantiauy co which longitudinally engages a s'gain in the,

of'the other gear ing tool having along.

ously' cut or groundwitha rotary cutting rpose of my invention is topro-v of space and anose of the invention is provide methods for bothsides of a tooth f the character de- A further object is tosimultaneously forming space of a bevel'gear o scribed.

, I A still f-urtherobject of theinvention" is to provide gears havingtooth surfaces derived from spherical surfaces. 1

- Thepurposesof my invention are in short, increased production, andimproved quality. My invention will be explained with ref erence to theaccompanying drawings, in which: I

Fig.1 is a plan view of a crown gear shown partly in section taken alongits pitch plane, and: showing teeth constructed according to myinvention. Figs. 2 and 3 are sections along I merely i Fig.4 is an eleof the crown gear shown i is an :elevational view of a partly out blankanda section ofa rotary cutter engaging two tooth sides ofthe blank, theteeth of said blank correspondingto the, form of crown gear shown inFigs. 1 an front 'elevational view, partly in section, showing a gear,"adapted-to mesh with the pinion illustrated in Fig. 5, being ground.Fig.7 is a plan view partly in section of a device for generating bevelgears according to my invention, the basic crown gear beingofsl'ightlymodified form as compared with Fig l.- Fig: 8 is a frontelevational view, partly in section of the device shown in Fig. 7.Figures 9 to 12-are' axial sections of rotary cutting tools, as may beused according to my invention. j Fig. 13 is a development of the pitchcones of two gea'rsof a pair, shown in engage1nent.Fig. '14: is adevelopment of the pitch cones of a p fied form, as compared with Fig.13. Fig. 15 is a plan view of a; bevel gearco'nstruct'ed according tomyinvention. Figs, 16 and 1 7 are axial sections; through-face millingcutterssuch as might -ing gears according to my invention, Fig. 18 .is'a plan view of theffacemill shown in-Fig. 16 loolrin'g 'in' thedirection of its'axis; and Fig; 19'is a similar view of the face millshown in Fig. 17. r

llustrated for explanatory purposes.

vational view partly in section n'Fig. 1. .Figi'5.

dfl. Fig. 6.is a

air of gears of a mod1 1 beemployed in producthe pitch planes of othercrown gears It is customary to define and describe bevel gearing bycharacterizing the crown gear, that is a particular bevel gear of asystem of bevel gears, whose pitch cone has a cone angle of 90 or nearly90. The pitch surface of a crown gear is, therefore, a. plane, or nearlya plane.

Referring to Fig. 1, and particularly to the left part thereof the viewshows a plan view, looking at right angles tothe said pitch plane of acrown gear, and the right part of Fig. 1 is a sectional View takenthrough its pitch plane. 1 denotes the axis of the crown gear, the teeth2 of which extend from the outside periphery 3 to the inside periphery4c. The toothed portion consists of the convex sides 5, 5, 5 of thecrown gear teeth, of the tips 6, 6, 6", of the concave sides 7, 7, 7 ofthe crown gear teeth, and of the tooth bottoms 8, 8, 8, which are shownslightly shaded, to distinguish them from the tips. The pitch lines 9and 10 are shown in dot and dash lines in the View On the left, and thepitch lines 9, 9 and 10, 10 are shown in full lines in the section onthe right. The pitch lines shown in Fig. 1 are arcs of circles ofcenters 11, ll, 11 and 12, 12, 12", the center of a mean circle 13 beingat 14., on normal line 15. The convex pitch lines 9 and the concavepitch lines 10 are parts of equal circles, which are angularly displacedabout axis 1' from each other. In other words the angle, for which oneside is displaced from the other side of a tooth, is the same at variousdistances from the apex 1. referred to as the angular tooth thickness inthe following, or angular width of space respectively. The crown gearshown in Fig. 1 has a constant angular tooth thickness and angular widthof space.

Figs. 2 and 3 are shown for comparison to illustrate teeth, of constantangular thickness, which are dilferently curved in longitudinaldirection. The pitch lines 20 and 21 of the crown gear shown in Fig.2are involutes, corresponding to a base circle 22. The (normal)tooththickness 23 is therefore constant,

and the same at various distances 24, 24 from apex 25, as well known tothose skilled in the art. The required (normal) tooth thickness, namely,depends not only on the distance from the apex, but also on theinclination of the teeth, that is on their spiral angle. The involutebeing a curve of comparatively sharp curvature, the tooth inclinationchanges rapidly along the tooth, and makes up for the diflierence inapex distance, so that teeth of constant thickness result. v

In a limited range the involute 26 can be approximated by circle 27,whose center 28 1s situated on normal line 29, at the point oftangencyof the normal line withbase circle 22. Gears with such circular teethapproximate the qualities of gears provided with teeth extending alonginvolutes longitudijThe angle, 16 in Fig. 1, will be.

nally; that is their normal tooth thickness is substantially constant.This would make it possible to simultaneously cover and represent bothsides of a crown gear tooth with a rotary cutting tool, whose axis isperpendicu lar to the pitch plane of the crown gear. In this way bothsides of a tooth space of a blank can be simultaneously formed in agenerating roll, but the resulting tooth shape is not so desirable. Suchgears have a constant dedendum, and'consequently a varying dedendumangle, which increases with decreasing apex distance.

The crown gear shown in Fig. 3 is provided with teeth of constantinclination with respect to the apex radius. The pitch lines 30 and'31are logarithmic spirals, each spiral having the quality of including thesame angle with every radius. The tooth thickness 32 is thenproportional to the apex distance 33, in analogy to .the conditionsexisting on straight teeth of bevel gears. The logarithmic spiral can beapproximated by its curvature circle. Thus spiral 34 can be closelyapproximated by circle 35 whose center 36 is situated on normal line 37.It will be noted that circle 35 is much larger than circle 27'of Fig. 2.

When it is attempted to simultaneously cover both sides of a such acrown gear tooth 5 with a rotary cutting tool, and to simultaneouslyform both sides of a tooth space of a blank, it will be found thatthe'axis of said decreases rapidly at decreasing apex distance.

While the dedendum should decrease about in proportion to theapexdistance, it decreases nearly twice as fast at standard toothproportions. This is also undesirable.

It will be noted however that here the dedendum angle of a blankdecreases at decreasing apex distance, while in the case of Fig; 2

the dedendum angle increases at decreasing apex distance, when in eithercase both Sides of a tooth space are simultaneously formed. Between thetwo cases there is necessarily a case, where the dedendum angle of ablank remains substantially constant, even when 1 5 two tooth sides aresimultaneously formed by a single rotary cutting tool. This case hasbeen illustrated in Fig. 1. It is by far preferred over the embodimentsof my invention shown in Figs. 2 and 3, and will be more fully describedand explained in the following. The diameter of circle 13 is between thediameters of the circles 27' and 35, and its center 14 is locatedbetween their centers 28 and 36. p

' The crown gear teeth shown in 2 are not tapered longitudinally. Theteeth shown in Fig. 3 are substantially tapered in longitudinaldirection. In the intermediate case of Fig. 1 the teeth are only verymoderately 13- normal profiles nsets tains apex 41. A projectionof theprofile of the tip surface 6 of of the crown gear preferably passesthrough, apex 41, as shown, thus constituting a constant addendum angle42 at all distances from apex 41. The addendum angle of the crown gearcorresponds to the dedendurn angle of bevel gear blanks, which angle issubstantially constant, according to the preferred embodiment of myinvention. r

Two slightly modified teeth 43 and 44 are shown in normal section inFigure 4 and Fig? provided with straighture 4a tooth '43 being 43 and43, while tooth 44 illustrates a slightly different formof tooth. whichis provided with a convex profile 44' and a concave profile 44. Eithershape, 43 or 44, may be adopted, but not both together.

It is not necessary that the tooth profile be 7 symmetrical with respectto the'pitch plane. The convex tooth surface 44 and th'e'concave toothsurface 44 hould however be identi cal, in the case oftheoreticalgearing, meshes with full line contact, and has a constantangular tooth thickness, as" shown in Fig. 1. Surface 44" convexspherical surface and 44" a'concave spherical surface of the sameradius. Inaddition to being identical, the surfaces '44 and 44" shouldalso be similarly disposed with respect to the pitch plane of the crowngear. In the case of spherical surfaces the centers of 44' and 44shouldbe the same distance below and above the pitch plane respectively, 1 andat the same distance from apex 41.

to Fig. 1. Fig.

Fig. 5, as an example, illustrates the. spherical tooth surfaces of thecrown gear, the lat ter being shown in axialsection at the right.

Theplan view of this crown gear is similar 5 "corresponds to a: sideelevational view taken from the right of Fig. 1. The convex toothsurfaces-5 '1) of the crown gear are parts of convex spherical surfaces,hose centers 45, 45", 45" are situated at a distance 46 below pitchplane 40, (see Fig. 5). -The centers 45 of the convex toothsurfaces'describea circle, which is shown in rojection'as a straightline 47 in Fig.5. T ie concave tooth' surfaces'6 (Fig.

. '1) "of the crown gear are similarly concave spherical surfaces of thesame radius. Their centers 48, 48, 48? are at 46abovepitch plane 40 (seeFig. 5 and describe another circle 49, which is symmetrically disposedto circle 47, 'with respect to pitch plane 40. T I H The pitch linesofthe teeth of the crown gear are the intersection lines 'o'fthe toothsarshown as line 40, which con- 'terparts.

bodiment of my invention,

which might be for instance tooth surfaces of thegear blank,

the cutting tool should be so inclined as to the same distance V faceswith pitch plane40, and are therefore identical circles 9,'9" and 10,

It will therefore be understood that theoretically accurate gears may beproduced from alright hand gear and an exactly symv metrical left handcrown gear of the described type.

In order to-produce a pair of mate gears one gear 56-is generatedaccording to the method illustrated in Fig. 5 from a basic crowngearsuch as shown in that figure and the other gear 120 of said pair isgenerated from a basic crown gear 121 of opposite hand. The two crowngears are When put together, so that the teeth of one gear go into thetooth spaces of the other crown gear and that their axes 1 and 122coincide, their tooth spaces and teeth will exactly fit each other. Whenthe crown gear shown side tooth surfaces, as is the preferred em theside tooth surfaces of the crown'gear 121 will also be spherical. Theconvex tooth surfaces of the crown gear 121 are convex sphericalsurfaces of centers 123, while the concave tooth exact counsur-- facesof this crown gear are concave spherical surfaces of centers 124. Thecenters 123 f One tooth side or preferablyboth sides of;

a tooth space of the gear 120 maybe produced in the same way has beenexplained with reference to the'production of the pinion 56 by thecutting tool 51, that is, by positioning a cutting tool to cover andrepresent a tooth surface orade jacent tooth surfaces of the crown gear121' 9; a rolling motion, between and by pro'vidin 'the gear blank andthe cutting too-lemployed,

in the manner of a gearmeshing with the by a rotarycutting tool, as

crown gear 121. The cutting tool employed in cutting the gear may beidentical with the tool 51 used in cutting order to cut simultaneouslytwo adjacent side the axis of p'ass through the center'123ofthe convexside of; the vcrown gear teeth as well as through the center 124 of theconcave tooth side. i

Instead of amilling cutter, I have shown in Fig. 6, a grinding wheelsuch as might be employed for grinding the tooth surfaces of the gear120 after the teeth have been cut or otherwise formed :The cuttingsurfaces the pinion 56. In

or a cutting surface of the grinding wheel 130 will represent toothsurfaces or a tooth surface of the crown gear 121. WVhere two toothsurfaces of the gear 120 are to be ground simultaneously, the cuttingsurfaces of the grinding wheel 130 will represent two adjacent toothsurfaces of the crown gear 121. In the embodiment illustrated, thegrinding wheel is of this form, the spherical cutting surface 131representing a convex side tooth surface of the crown gear 121 and thespherical cutting surface 132 representing a concave side tooth surfaceof said crown gear. The axis 138 of the grinding wheel is so inclined asto pass through the centers 123 and 124 of the convex and concave sidetooth surfaces of the crown gear. During the rotation of the grindingwheel about its axis 133, a relative rolling motion will be impartedbetween the wheel 130 and the gear 120 in the manner of a gear meshing.with the crown gear 121.

By the operation described, tooth surfaces will be ground upon the gear120 which are conjugate with the tooth surfaces produced upon the pinion56. The tooth surfaces of the pinion 56 maybe ground by a grinding wheelidentical with the wheel 130, the same relative motions being employeddescribed in connection with the cutting 0 he pinion by the tool 51. r

In the following it will be explained how two tooth sides of either arighthand or a left hand bevel gear may be simultaneously formed. V7 henboth sides of a crown gear tooth shall be simultaneously represented andcovered by a rotary cutting tool, the axis 50 of said cutting tool mustbe so inclined as to pass through the center of the convex sphericaltooth surface and also through center 18 of the concave spherical toothsurface. In other words axis must be the connecting line between thesaid two centers, see F 5. A milling cutter is shown in such position,in this figure, partly in elevation and partly in section. It consistsof a body port-ion 51 and a number of inserted blades, which constitutean outside cutting surface52, a cutting tip 53 and an inside cuttingsurface 5 1. The outside and the inside cutting surfaces, 52 and 5e,respectively, are convex and concave spherical surfaces, respectively,having the same radius as the tooth surfaces to be represented,theircenters coinciding with the centers 45 and 18 respectively, duringthe cut. Nhen the cutter diameter has been suitably selected, asubstantially constant dedendum angle 55 will be produced on a gearblank The tooth surfaces of gear be are produced by providing arolling-generating motion etween cutter and blank, while rotating thecutter about its axis. The generating motion represents a rolling actionbetween the blank and the crown gear, of which the cutter as ftconstitutes a tooth, as familiar to those skilled in the art. I

It will be noted, that it is thus possible to produce theoreticallyaccurate bevel; gears having a substantially constant dedendum angle,thatis having a tooth bottom running towards the apex; and moreover thatit is possible to form both sides of a tooth space sin'iultaneously onsuch theoretically accurate gears.

Figures 7 and 8 show a form of crown gear and illustrate a slightlymodified way of generation. The cutter represents and constitutes atooth of a nominalcrown gear 61, the pitch surface 62 of which is notexactly a plane, but a conical surface, having its cone angle 63slightly smaller than 90. It'usually differs from a right angle by thededendum angle 64 of the blank 65, see Fig.7. The tip surface of thiscrown gear is a plane.

This form of crowngear is used by a well known machine, namely theGleason spiral bevel gear generator. My invention provides a toothshaped for this method of generation, so that in addition both sides ofa tooth space of a blank can be simultaneously formed.

A crown gear used according to this embodiment of my invention andrepresented by a cutter 60 is shown in Fig. 8 in a view along its axis66. The tip surfaces 67, 67, 67 of this crown gear are of constantwidth. They are shown slightly shaded for convenience. In the caseillustrated in Fig. 7 the apex 68 is outside of the tip circle '69 ofthe cutter, and situated in the plane of the tip.

In this method of generation just described the axis 70 ofthe rotarycutting tool 60 is set parallel to the axis 66 of the generating crowngear, whereas in Fig. 5 the axis of the cutting tool is inclined withrespect to the axis 1 of the crown gear. The method of generation shownin Figs. 7 and 8 is closely approximate, whereas the methodcorresponding to Fig. 5, may be theoretically accurate, as stated.Thecutter diameter required for 'simultaneousforming oftwo toothsurfaces may in either case be determined by the known methods ofdescriptive geometry. When all other data are the same,

slightly modified the cutter diameter will be found to be very nearlythe same for either form of crown gear. The principle is to curve theteeth longitudinally to such an extent, that'the resultingteeth andtooth spaces are only moderately tapered in longitudinal direction, justso much as will be providedby a rotary cutting tool, when positionedsoas to produce the required dedendum angle;

Apart from the selection of the cutter diameter and the determination ofthe cutter setting, the generation can entirely bekept along the knownlines. I

In order to carry out this purpose a milling cutter 60 is rotatablyfixed to a cradle 71,

V @The mat gea /may e which contains V-shaped circular projections 72,which may slide along stationary gu d wees 173 of the frame 74: of themachine. The guidances permit the cradle to be angularly .fed, aboutvaxis v66, which, is parallel to the cutter axis 70 and passesthrough theapex 68 ofblank 65, after the latter has been set inposition. r Y 7 Agear blank 65 is rotatably held in stationary bearings -7 5 whi'ch. are"so positioned, that.- the axis 76 of the blank intersects axis in ap x68-1 Wh l ft cu e ot ted, the b nk6 5 a he adl -T P fo m g n crating--roll, which: JQIlSists in an angular ie nf th adl ab a is 5 an in a rp d g ang la tur meta of he blank about its own axis 76.

sam ma hin -in he same W ymathema lca ly cu I t o urfa es, however, the.basic rown gears must be exact Q n e -na s s ne an r- I t a the pitchsurfacegof the crown gear upon which the mate gear is rolled should belarger th n 1 by thesam a gl he he mt rar q wn gear les ith l 0 lfl reetea s l a ipredu d as h iec wnsear a exa t ys e enta 'and thesum of theirpitchangles equal to Icing; a t We av dine .11 vvmy i v nt on an :he r rwithin broad limits. Fig. 9 shows a milling .u w stra ht se tin in o 8 a81, which,.as arule, are inclined in' a slightly ltl ef i d er e 'e eit-i si te @1882 inv o r p sw 1t l p s nt Practice.

The milling cutter of: 10 an ,outer inward profile 90. Suchacutter maybensed n a s Iconveiiprofile 83 and aninnerconcav'e profile 84;.Theseprofiles are substantiallyarcs of:

circles, .having centers v85q and-l86 Qan'd radii s a sllzi s m sa mi li-put gwithconcave'outward profile .89 and'concave (for{simultaneouslyputting Qboth sides of a tooth space withoutthegenerating .roll; 'In

gear :pairs of vlargelredu ction, .as are {used n the :rear axle drivesof motor cars,

I I r gear of; .the pair may be. advan- 1, :ageouslycutwitha formed cuttr {the toolmldths l n s approa h d to.- ward each other until fullcutting de th j i reached. iFig. 12 showsalrotary cuttingtool andspecially. according tojthe It? i t i pq i the To Pro u e centrating deinf ac cordancef with developments have a common "centerfloirj apex at100. The shaded areas 101, 102, 103 a11e the sections of the pitch .coneof one gear with its teeth, 101 1'02 being the pitch line a of theconvex tooth sides and 101,f102 103", being the pitch line'sfof theconcave tooth sides. The areas 101, 105, 106 are the tooth sections ofthe pitch cone of the other gear of said pair, 104, 105 and 104", 105

b ing the convex and concave pitch lines, r spectively. Y

It will be "noted that the areas do not entirely fit each other. vTheconvex pitch lines- 101', l05fareisomewhat more curvedthan the concavepitch lines 102, 103", as shown'in exaggeration in Fig. 13. The toothhearing has, therefore, a I tendency to beconcentrated in the middleof'the teeth. Thisis an asset as long, as it is not exaggerated,inasmuch as it allows for slight inaccuracies in the mounting of thegears. When this tendency ofconthe tooth bearing however be comes toopronounced, as is the case for big pitchesandsmall tooth numbers of thecorre 99 spending crown gears, it is preferable topro vide acorrection,such correction being made possible by using a two gears of a pair.Gears correspondingto Fig; 13 are produced whenusing the same cutter onbothgears of a pair. -When using two cutters, gears can different cutteron the 1 duced, the driving sides of which may fit each other as closelyas desired. The unimr'- .portant reverse sides of the teeth willthenalone have concentrated tooth bearingl the two cutters used for thispurpose aregof slightly difierent diameter, the outside diameter of onecutter corresponding to inside diameter of the other cutter. i Fig. 14:isa development ofthe pitchcones of a pair of gearsmade after the mannerjust described, and having the areas 109'and 107, and 108 entirely. fiteach other, while .the contact between the areas 106 and 109, 107and.;110, 108 and 111 is concentrated in their mid-portion. In eithercase, shown in the Fig. 13 and Fig. 14 respectively, both sides of atooth space can be simultaneously formed according to my invention. aThe gears of a pair formed according to my invention may be providedwith equal or unequal addenda inthesame way as vthat (of other spiralbevel gears. Unequal addenda'are frequently recommended for largeQreductions, thepinion being provided with an increased addendum. c

I The terms, angular width of space and angular tooth thickness, applyalways to the middle ofthe tooth height, unless difierently .specified.'In the case of equal addenda on both gears'of a pair the said termsrefer consequently tothe pitch surface. f In, the case of a'painofngeangular width of space andthe angular tooth thickness are measuredsomewhat outside o'f ars with unequal addenda, the

the pitch surface, namely midway between the outside cone and the bottomcone.

Fig. 15 illustrates a gear made according to my invention, in a Viewtaken at right angles to the bottom 112 of'a tooth space. It can beconsidered as a gear formed in a generating roll, or also as a gear cutwith a formed milling cutter without generating motion; The toothbottoms are of equal width 113 along their whole length, and arepreferably cut towards the apex. In other words the tooth bottom issituated substai generating process, they constitute surfaces derivedfrom two coaxial surfaces of revolution.

Fig. 16 shows a type'of milling cutter 135 r such as may be used forproducing gears according to this invention. The cutter'135 is providedwith an outside cutting face 136 ofconvex profile, a cutting tip 137,and an inside cuttingface 138 of concave profile. Inserted blades 139are suitably fastened to the body 1400f the cutter. The blades 139 arerelieved back of their cuttin edges in a direction parallel to thecutter axis 141. 142 denotes a cutting profile such as would resultafter the cutter has been sharpened a-number of times. The profile 142is identical in form to the profile '136'137138 and is merely displacedin an axial direction with reference to this latter profile.

Fig. 17 illustrates a milling cutter which is provided with a somewhatdifferent kind of relief. The inclination of the convex outslde profile145 with respect to the cutter axis 146 is substantially different fromthe indi nation of the concave inside profile 147. In such cases, therelief provided extends in a direction somewhat oblique to the cutteraxis 146 as indicated by arrow 148. A profile such as would be formedafter sharpening is shown in dotted lines at 149. This profile isdisplaced not only in an axial direction but inwardly also.

A partial view in the direction of the cutter axis of the tool 135 isshown i Fig. 18,

while Fig. 19 shows a corresponding view of the tool shown in Fig. 17.The relief lines 150 extend inwardly, while the relief lines 151 remainat a constant distance from the cut-teraxis 141.

It will be understood that suchxchanges and modifications may be made inmy invention, as fall within the scope of the appended claims.

'Iclaim': H 1.1A pair of spiral bevel gears, either gear of said pairhaving tooth spaces whosesides and bottoms are conjugate to, butdifferent from, coaxial surfaces of revolution, said surfaces bemg ofsuch diameter, that the sum of I the dedendum angles of said pair issubstantially the same on the large end and on the sinalljend of theteeth. I

2. A pairof spiral bevel gears, either gear of said pair having toothspaces whose sides and bottoms are conjugate to, but different from,coaxial surfaces of revolution, said different from the axis, of eithermember of a said pair, and the tooth bottoms of said pair being inlinewith its apex. V A

j 4. A pair of spiral bevel gears, each gear of saidpair having toothspaces'whose sides and bottoms are conjugate to, but different from,coaxial surfaces of revolution,said sidesubeing conjugate to convex andconcave spherical surfaces respectively, and the sum of the dedendumangles ofsaid pair being substantially the same onthe large end and onthe small lend of the'teeth. a j

' a 5. A pair. of spiral bevel gears, each gear of said pair havingtooth spaces whose sides and bottoms are conjugate to, but differentfrom, coaxial surfaces of revolution,'saidvsides being conjugaterespectively toa convex and a concave spherical surface of substantiallyequal radii, the tooth bottoms of said pair being in line with theirrespective apexes.

6. A pair of spiral bevel'gears, each gear. of said pairhaving toothspaces whose sidesand bottomare conjugate to coaxial surfaces ofrevolution, said surfaces being rotatable about an axis inclined totheir ownaxis and different from the. axis of either member of said.pair, said surfaces containing curved profiles and being ofsuchdiameter, that the sum of the dedendum angles .of. said pair issubstantially. on the large end and on the .small end of the teeth.

7 A pair of longitudinally curved tooth tapered gears, each of which hassides conjugate to, but different from, surfaces of revolution,alternateside surfaces being conjugate respectively. to convexandconcave spherical surfaces, each gear having generated tooth surfacesconjugate to the tooth surfaces of a basic gear other than its-mate. H

8. A pair of longitudinally curved tooth tapered gears, each of whichhas tooth spaces jwhose sides are conjugate to, but different from,coaxlal surfaces of rev0lut1on, said, sides bemg con ugate respectivelyto convex and concave spherical surfaces of substantial- I 1y equalradii, each gear having generated tooth surfaces conjugate to the toothsurfaces of a basic gear other than its mate.

5 9. A pair of longitudinally curved tooth tapered gears, which haveside tooth surfaces conjugate to the side tooth surfaces ofcomplementary basic gears, adjacent side tooth surfaces of each basicgear being, respective- 0 1y, coaxial convex and concave sphericalsurfaces of revolution.

In testimony whereof I affix my signature. I ERNEST WILDHABER.

